Hypergendered Logic Source
Hypergendered Logic — Page 120
PA(PA(x)) remains noncanonical in core HGL. In the allowed expression, the inner Boolean tree may be arbitrarily deep. PA treats the complete tree as the designated developmental causal basis. PA irreducibility therefore applies to the whole nested condition. This gives PA a developmental metaexpressive role: the inner logical condition can specify a complex rule/constraint basis for how anatomy and physiology can be developmentally expressed, while the outer PA asserts necessary developability due irreducibly to that basis. 231. PA irreducibility still blocks decomposition PA(A AND B) ≠ PA(A) AND PA(B), in general. PA(A OR B) ≠ PA(A) OR PA(B), in general. PA(NOT A) ≠ NOT PA(A), in general. The metaexpressive reading strengthens rather than weakens these laws. If the entire inner logical function configures one developmental causal basis, decomposing it can erase the interaction rule that makes the basis what it is. 232. Two different metaexpressive layers PA and Γ are both metaexpressively important, but they do not operate at the same type. PA metaexpression: developmental-causal. It concerns the causal logical basis under which anatomy/physiology is necessarily developable. Γ metaexpression: phenotype-regulatory. It concerns the stage-global rules under which concrete physical phenotype is expressible. developmental causal condition --PA--> developmental architecture --Γ_n--> admissible phenotype expression-space. This sequence is schematic rather than a claim that every phenotype is a deterministic one-step output of PA. The important point is type order: developmental causal structure and phenotype metaexpression are distinct causal/logical layers. 233. Stage-relative phenotype modality Modal logic becomes natural once Γ is understood as a rule-system over phenotype-space. HGL therefore defines stage-relative biological necessity and possibility. □^F_n φ := φ holds in every phenotype realization permitted by Γ^F_n. ◇^F_n φ := φ holds in at least one phenotype realization permitted by Γ^F_n. □^M_n φ := φ holds in every phenotype realization permitted by Γ^M_n. ◇^M_n φ := φ holds in at least one phenotype realization permitted by Γ^M_n. These are not claims about unrestricted logical, metaphysical, or omniversal possibility. They are typed claims about biological phenotype expressibility under one current Archstage rule-regime. 234. Required, permitted, and forbidden phenotype statuses For a phenotype proposition p at Stage n, Γ can assign at least three basic modal statuses. Required: □^F_n p Permitted: ◇^F_n p AND NOT □^F_n p
Source Canon: Verbatim mathematical and modal logic. Interactive navigation and operator lookups available at /#hgl-part:120.